Question

In one town, the number of burglaries in a week has a Poisson
distribution with mean μ = 4.5. Let variable x denote the number of
burglaries in this town in a randomly selected
**month**. Find the * smallest
usual* value for x.

(HINT: Assume a month to be exactly 4 weeks)

Answer #1

1. An automobile manufacturer has determined that 33% of all gas
tanks that were installed on its 2015 compact model are defective.
If 16 of these cars are independently sampled, what is the
probability that at least 6 of the sample need new gas tanks?
2. Use the Poisson Distribution Formula to find the indicated
probability: Last winter, the number of potholes that appeared on a
9.0-mile stretch of a particular road followed a Poisson
distribution with a mean of...

1. For a binomial distribution, if the probability of success is
0.621 on the first trial, what is the probability of success on the
second trial?
2.A company purchases shipments of machine components and uses
this acceptance sampling plan:
Randomly select and test 32 components and accept the whole batch
if there are fewer than 5 defectives.If a
particular shipment of thousands of components actually has a 5.5%
rate of defects, what is the probability that this whole shipment
will...

1) Which of the following situations follows a Poisson
probability distribution? The number of patients who check in to a
local emergency room between 7 and 10 p.m. The number of foxes in a
one-acre field The number of MacBook Pros purchased at a particular
store in the first month after a newly released version The number
of children on a playground during a 24-hour period 2)The mean
number of burglaries in a particular community is μ = 3.4 per...

The number of houses sold by an estate agent follows a Poisson
distribution, with a mean of 2 per week.
a.Find the probability that in the next 4 weeks the estate agent
sells, 1 exactly 3 houses, 2 more than 5 houses.
The estate agent monitors sales in periods of 4 weeks.
b.Find the probability that in the next twelve of these 4 week
periods there are exactly nine periods in which more than 5 houses
are sold.
The estate...

The number of trees per acre in the Lassen National Forest in
California follows a Poisson distribution with a rate of 100 trees
per acre. Let the random variable X count the number of trees per
randomly selected acre of the Lassen National Forest
A) State the distribution of the randomly variable defined
above
B) Compute and interpret P(X=107)
C) Compute the probability that in a randomly selected acre of
the Lassen National Forest there are at most 90 trees...

Suppose that the number of eggs that a hen lays follows the
Poisson distribution with parameter λ = 2. Assume further that each
of the eggs hatches with probability p = 0.8, and different eggs
hatch independently. Let X denote the total number of
survivors.
(i) What is the distribution of X?
(ii) What is the probability that there is an even number of
survivors?
(iii) Compute the probability mass function of the random
variable sin(πX/2) and its expectation.

a) The defect rate for a wire making process has a
Poisson distribution with 1.23 defects per 1000 feet. Let X be the
number of defects widgets in a randomly-selected 1000-foot length
of wire. What is the probability that there will be no defects in
that length of wire? State your answer rounded to three decimal
digits.
b) Let X be the net weight of a randomly-selected cereal box.
The distribution of net weight for this filling process is
uniformly-distributed between...

The number of times a geyser erupts in one day follows a Poisson
distribution with mean 2.5. On a randomly selected day:
(a) what is the probability that there are no eruptions? (b)
what is the probability of at least 3 eruptions?

Suppose that the number of eggs that a hen lays follows the
Poisson distribution with parameter λ = 2. Assume further that each
of the eggs hatches with probability p = 0.8, and different eggs
hatch independently. Let X denote the total number of survivors.
(i) What is the distribution of X? (ii) What is the probability
that there is an even number of survivors? 1 (iii) Compute the
probability mass function of the random variable sin(πX/2) and its
expectation.

Topic: Poisson Probability Distribution
The Poisson Distribution is a discrete probability distribution
where the number of occurrences in one interval (time or area) is
independent of the number of occurrences in other intervals.
April Showers bring May Flowers!! Research the "Average Amount
of Days of Precipitation in April" for a city of your choice.
Introduce
Introduce the City and State. Let us know a fun fact!
Tell us the average number of days of precipitation in that
city for the...

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